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Introduction to Calculus and Classical Analysis

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Involving rigorous analysis, computational dexterity, and a breadth of applications, this text is ideal for an undergraduate honors calculus course or for an introduction to analysis. This fourth edition includes corrections as well as some additional material.

Some features of the text:

•The text is completely self-contained and starts with the real number axioms;

•The integral is defined as the area under the graph, while the area is defined for every subset of the plane;

•There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero;

•There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more;

•Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals;

•self-contained treatment of the fundamental theorems of calculus in the general case using the Sunrise Lemma

•There are 450 problems with all the solutions at the back of the text.

Author: Hijab Omar
Publisher: SPRINGER
Pages: 427
ISBN: 9783319803456
Cover: Paperback
Edition Number: 4
Release Year: 2016

Omar Hijab is Professor of Mathematics and Associate Dean for Faculty Affairs, Information Technology, and Operations in the College of Science and Technology at Temple University. He received his Ph.D. in Mathematics from the University of California, Berkeley, and has served previously as Chair of the Department of Mathematics at Temple University. His research interests include systems theory and control; probability theory and stochastic processes; differential equations; mathematical physics; and optimization.

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